Motility-Induced Pinning in Flocking System with Discrete Symmetry

Chul-Ung Woo; Jae Dong Noh

arxiv: 2403.10106 · v2 · submitted 2024-03-15 · ❄️ cond-mat.stat-mech · cond-mat.soft

Motility-Induced Pinning in Flocking System with Discrete Symmetry

Chul-Ung Woo , Jae Dong Noh This is my paper

Pith reviewed 2026-05-24 02:29 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.soft

keywords motility-induced pinningactive Ising modelflocking transitionpolar orderself-propelled particlesinterface pinningdiscrete symmetryMonte Carlo simulation

0 comments

The pith

Pinned interfaces grow macroscopically and suppress polar order in the active Ising model when particle diffusion is much slower than self-propulsion.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines the active Ising model of self-propelled particles with discrete symmetry, which was previously shown to have a liquid-gas flocking transition but with metastable polar order due to droplet excitations. Through Monte Carlo simulations, it identifies a motility-induced pinning transition at intermediate alignment strengths where colliding domains form traveling local regions and interfaces between them become pinned by resonating particle motion across the boundary. An approximate analytic theory describes the growth and shrinkage of these pinned interfaces, showing that they expand to macroscopic size in the regime of low diffusion relative to propulsion, which prevents the establishment of long-range polar order.

Core claim

In the active Ising model, interfaces between colliding domains of self-propelled particles become pinned through a resonating back-and-forth motion of individual particles across the interface; as alignment interaction strength increases, these pinned interfaces grow to macroscopic size when the diffusion rate is sufficiently smaller than the self-propulsion rate, rendering polar order short-ranged in both space and time.

What carries the argument

The resonating back-and-forth motion of self-propelled particles across domain interfaces, which stabilizes pinning and drives the growth dynamics of pinned regions.

If this is right

Polar order remains short-ranged in both space and time for intermediate alignment strengths due to traveling local domains.
A numerical phase diagram separates regimes of unpinned traveling domains from pinned macroscopic interfaces.
The approximate analytic theory predicts growth versus shrink dynamics of pinned interfaces as a function of alignment strength and diffusion rate.
Polar order is prevented when diffusion is sufficiently slower than self-propulsion.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The pinning mechanism may generalize to other discrete-symmetry active systems where interface stability depends on particle crossing rates.
In the opposite regime of faster diffusion, unresolved growth behavior could still limit the range of polar order through different dynamics.
Experimental realizations with colloidal or granular particles could test the predicted dependence on the diffusion-to-propulsion ratio by varying temperature or drive strength.

Load-bearing premise

The observed pinning and its growth to macroscopic scale in simulations reflect the thermodynamic limit rather than finite-size or transient effects, and the approximate analytic theory captures the interface dynamics without additional fitting parameters.

What would settle it

Simulations in significantly larger systems that check whether pinned interfaces continue to grow without bound (or saturate at a finite fraction of system size) specifically when the diffusion-to-propulsion ratio is decreased below the reported threshold.

Figures

Figures reproduced from arXiv: 2403.10106 by Chul-Ung Woo, Jae Dong Noh.

**Figure 1.** Figure 1: ), which was first reported in Ref. [50]. The system, starting from an ordered initial state, evolves into a state with multiple traveling droplets, nucleated spontaneously. These droplets grow and merge into larger ones. At the same time, they also suffer from spontaneous nucleation of droplets of opposite polarization, and break up into smaller pieces. This competition between growth and break-up driv… view at source ↗

**Figure 3.** Figure 3: FIG. 3. (a) Propagation speed of a droplet from the MC [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 2.** Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

read the original abstract

We report a motility-induced pinning transition in the active Ising model for a self-propelled particle system with discrete symmetry. This model was known to exhibit a liquid-gas type flocking phase transition, but a recent study reveals that the polar order is metastable due to droplet excitation. Using extensive Monte Carlo simulations, we demonstrate that, for an intermediate alignment interaction strength, the steady state is characterized by traveling local domains, which renders the polar order short-ranged in both space and time. We further demonstrate that interfaces between colliding domains become pinned as the alignment interaction strength increases. A resonating back-and-forth motion of individual self-propelled particles across interfaces is identified as a mechanism for the pinning. We present a numerical phase diagram for the motility-induced pinning transition, and an approximate analytic theory for the growth and shrink dynamics of pinned interfaces. Our results show that pinned interfaces grow to a macroscopic size preventing the polar order in the regime where the particle diffusion rate is sufficiently smaller than the self-propulsion rate. The growth behavior in the opposite regime and its implications on the polar order remain unresolved and require further investigation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper reports a motility-induced pinning transition in the active Ising model via interface resonance that can suppress long-range order in the low-diffusion regime, but the thermodynamic limit is not secured by scaling.

read the letter

The main thing to know is that this work identifies a regime in the active Ising model where interfaces between traveling domains pin due to particles resonating back and forth across them, which keeps polar order short-ranged when diffusion is much slower than self-propulsion. This is presented as distinct from the known liquid-gas flocking transition and the droplet metastability in prior studies on the same model. The simulations map a phase diagram for an intermediate alignment strength where this happens, and they flag the resonance as the pinning mechanism. An approximate analytic treatment of interface growth and shrink dynamics is added to support the numerics. The Monte Carlo runs are the clearest strength here; they are described as extensive and directly show the effect on finite systems along with the back-and-forth particle motion. The authors are also straightforward that the high-diffusion regime is left open. The soft spot is exactly the one in the stress-test note. The central claim requires that pinned interfaces reach a size that stays macroscopic as volume goes to infinity, yet the results are shown on finite lattices without reported scaling of steady-state interface length, domain number, or correlation length versus L. It remains possible that the pinning is a slow transient or finite-size crossover that would allow coarsening in the true thermodynamic limit. The theory being approximate adds to the caution. This is for people working on active matter and discrete-symmetry flocking models who want a concrete mechanism that can cut off order. It is worth sending to peer review because the simulations are substantive and the idea is worth testing, but any referee should press for finite-size scaling data and checks on whether the pinning survives extrapolation to large L.

Referee Report

2 major / 2 minor

Summary. The manuscript reports a motility-induced pinning transition in the active Ising model. Using extensive Monte Carlo simulations, it finds that for intermediate alignment interaction strengths the steady state consists of traveling local domains that render polar order short-ranged. Interfaces between colliding domains become pinned via a resonating back-and-forth particle motion; an approximate analytic theory is given for the growth and shrink dynamics of these interfaces. The central claim is that, when the diffusion rate is sufficiently smaller than the self-propulsion rate, pinned interfaces grow to macroscopic size and thereby suppress long-range polar order. A numerical phase diagram is presented; the opposite (high-diffusion) regime is left unresolved.

Significance. If the pinning mechanism and its macroscopic growth survive the thermodynamic limit, the result would clarify the origin of short-ranged order in discrete-symmetry active systems and would complement existing work on metastable polar order. The combination of direct simulation with an analytic interface theory is a methodological strength.

major comments (2)

[Monte Carlo results and phase-diagram section] The central claim that pinned interfaces reach a macroscopic size that survives the thermodynamic limit (thereby preventing long-range polar order) rests on finite-lattice Monte Carlo data. No finite-size scaling analysis of steady-state interface length, domain number, or correlation length versus linear size L is reported, so it remains possible that the observed pinning is a slow transient or finite-L crossover. This issue is load-bearing for the abstract's statement on macroscopic growth in the low-diffusion regime.
[Analytic theory section] The analytic theory for interface growth/shrink dynamics is labeled approximate. The manuscript should state explicitly which approximations are made, whether any effective parameters are introduced by the approximation, and whether those parameters alter the predicted pinning threshold or growth law in the low-diffusion regime.

minor comments (2)

The abstract states that the high-diffusion regime remains unresolved; a short paragraph explaining why this regime is left open would improve clarity.
Simulation figures and the phase diagram should include error bars or estimates of statistical uncertainty.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We respond to each major comment below and will revise the manuscript accordingly.

read point-by-point responses

Referee: [Monte Carlo results and phase-diagram section] The central claim that pinned interfaces reach a macroscopic size that survives the thermodynamic limit (thereby preventing long-range polar order) rests on finite-lattice Monte Carlo data. No finite-size scaling analysis of steady-state interface length, domain number, or correlation length versus linear size L is reported, so it remains possible that the observed pinning is a slow transient or finite-L crossover. This issue is load-bearing for the abstract's statement on macroscopic growth in the low-diffusion regime.

Authors: We agree that the absence of finite-size scaling leaves open the possibility of finite-L effects or transients. In the revised manuscript we will add finite-size scaling analysis of the steady-state interface length, domain number, and correlation length versus L, performed in the low-diffusion regime. Additional simulations at larger L already indicate that the macroscopic pinning persists, but the systematic scaling will be included to address this point directly. revision: yes
Referee: [Analytic theory section] The analytic theory for interface growth/shrink dynamics is labeled approximate. The manuscript should state explicitly which approximations are made, whether any effective parameters are introduced by the approximation, and whether those parameters alter the predicted pinning threshold or growth law in the low-diffusion regime.

Authors: We acknowledge that the approximations underlying the analytic interface theory require explicit enumeration. In the revision we will list the approximations (mean-field treatment of local densities and neglect of higher-order correlations), confirm that no auxiliary effective parameters are introduced, and demonstrate that the predicted pinning threshold and growth laws in the low-diffusion regime are unaffected by these approximations. revision: yes

Circularity Check

0 steps flagged

No circularity; results from independent simulations and approximate theory

full rationale

The paper reports Monte Carlo simulations demonstrating traveling domains and pinned interfaces, plus an approximate analytic theory for interface growth/shrink dynamics. No load-bearing step reduces a claimed prediction or first-principles result to a quantity defined in terms of its own fitted inputs or prior self-citation. The central claim (macroscopic pinning preventing polar order at low diffusion) is presented as an outcome of the simulations and theory rather than a tautological re-expression of inputs. Self-citations, if present, are not invoked to forbid alternatives or force the result by construction. This is the common honest outcome for simulation-driven work.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on Monte Carlo sampling of the active Ising model and an approximate analytic treatment of interface dynamics; model parameters such as alignment strength, diffusion rate, and self-propulsion rate are varied but not fitted to external data within the reported results.

free parameters (2)

alignment interaction strength
Varied as the control parameter separating traveling-domain and pinned regimes.
diffusion rate relative to self-propulsion
Key ratio determining whether pinned interfaces grow macroscopically.

axioms (1)

domain assumption The active Ising model on a lattice with discrete directions and Metropolis Monte Carlo dynamics faithfully represents the intended self-propelled particle system.
Invoked throughout the simulation protocol described in the abstract.

pith-pipeline@v0.9.0 · 5724 in / 1341 out tokens · 21960 ms · 2026-05-24T02:29:33.730340+00:00 · methodology

discussion (0)

Reference graph

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Motility-Induced Pinning in Flocking System with Discrete Symmetry

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Namely, all lattice sites are occupied by+ particles of mean densityρ0 except for those within a(2 × l) rectangle

The system is prepared to be in an ordered state with a PI of lengthl being implanted. Namely, all lattice sites are occupied by+ particles of mean densityρ0 except for those within a(2 × l) rectangle. They are occupied by ρ′ 0 (> ρ0) particles whose spin states are+ in the (1 × l) column on the left and− in the (1 × l) column on the right

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The occupation numbers at sites along the domain boundary are required to be larger than a cutoff valueρcutoff = 5ρ0

A PI is identified as an interface between positively and negatively polarized domains. The occupation numbers at sites along the domain boundary are required to be larger than a cutoff valueρcutoff = 5ρ0

work page
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To reduce an artifact from short-time fluctuations,ln represents a running average over the time intervaltn−n0 < t < t n with n0 = 10

During simulations up to107MCS, we record the time trajectory{ln = l(t = tn)} of the PI length at discrete time steps tn = nτ0 with n ∈ Z and τ0 = 103. To reduce an artifact from short-time fluctuations,ln represents a running average over the time intervaltn−n0 < t < t n with n0 = 10

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The growth rateWg(l) and the shrink rateWs(l), per unit MCS, are given byNl→l+1/Tl and Nl→l−1/Tl, respectively, which are then averaged over more than103 independent trajectories

Given a trajectory{ln}, we countNl→l±1, the number of jumps inln from l to l ± 1, andTl, the total time span in which ln = l. The growth rateWg(l) and the shrink rateWs(l), per unit MCS, are given byNl→l+1/Tl and Nl→l−1/Tl, respectively, which are then averaged over more than103 independent trajectories. 2 0 5 10 15 20 l 10−7 10−5 10−3 10−1 W (l) (a) Wg W...

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Given a trajectory{ln}, we countNl→l±1, the number of jumps inln from l to l ± 1, andTl, the total time span in which ln = l. The growth rateWg(l) and the shrink rateWs(l), per unit MCS, are given byNl→l+1/Tl and Nl→l−1/Tl, respectively, which are then averaged over more than103 independent trajectories. 2 0 5 10 15 20 l 10−7 10−5 10−3 10−1 W (l) (a) Wg W...

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